infant school vs grade school

infant school and grade school both are nouns.

Word	Noun	Adjective	Verb	Adverb
infant school	Yes	No	No	No
grade school	Yes	No	No	No

As nouns, grade school is a hypernym of infant school; that is, grade school is a word with a broader meaning than infant school:

Other hypernyms of infant school include elementary school, grammar school, primary school.

infant school (noun)	grade school (noun)
British school for children aged 5-7	a school for young children; usually the first 6 or 8 grades